Posted: 05/08/2016 at 08:21
I don't think many people these days would class a garden of 80' by 50' in old money as being a 'small garden'. If that is the lawn area it's a substantial area to cut. Strimming or mowing, leaving the cut grass on the lawn will encourage a build up of thatch and that is detrimental to the lawn. Once it is fully under control you can leave the cuttings as long as you cut regularly.
As for the type of mower, how severe is the slope? Even wheeled mowers will be OK on a slight slope.
Any mower can be used without a grass box. With rotary mowers a flap generally comes down where the grass box would be to minimise the spray but you would probably get some. My Honda mower has a rubber 'skirt' at the back to stop that happening.